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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Horvath%2C+I&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Horvath%2C+I&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Horvath%2C+I&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2404.12298">arXiv:2404.12298</a> <span> [<a href="https://arxiv.org/pdf/2404.12298">pdf</a>, <a href="https://arxiv.org/format/2404.12298">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> Dirac Spectral Density in N$_f$=2+1 QCD at T=230 MeV </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Bonanno%2C+C">Claudio Bonanno</a>, <a href="/search/hep-lat?searchtype=author&query=D%27Elia%2C+M">Massimo D'Elia</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2404.12298v2-abstract-short" style="display: inline;"> We compute the renormalized Dirac spectral density in $N_f = 2+1$ QCD at physical quark masses, temperature $T = 230$ MeV and system size $L_s = 3.4$ fm. To that end, we perform a point-wise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of Dirac operator describing dynamic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.12298v2-abstract-full').style.display = 'inline'; document.getElementById('2404.12298v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2404.12298v2-abstract-full" style="display: none;"> We compute the renormalized Dirac spectral density in $N_f = 2+1$ QCD at physical quark masses, temperature $T = 230$ MeV and system size $L_s = 3.4$ fm. To that end, we perform a point-wise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a non-trivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently-proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical; (ii) improve the upper bound for IR-phase transition temperature $T_{\mathrm{IR}}$ so that the new window is $200 < T_{\mathrm{IR}} < 230\,$MeV; (iii) are consistent with non-restoration of anomalous U$_{\mathrm A}$(1) symmetry (chiral limit) below $T = 230$ MeV. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2404.12298v2-abstract-full').style.display = 'none'; document.getElementById('2404.12298v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 6 figures; v2: 8 pages, 7 figures, added results on the topological nature of the peak, other results and conclusions unchanged, version to appear in PRD</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2310.03621">arXiv:2310.03621</a> <span> [<a href="https://arxiv.org/pdf/2310.03621">pdf</a>, <a href="https://arxiv.org/format/2310.03621">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> Localized Modes in the IR Phase of QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Bhattacharyya%2C+N">Neel Bhattacharyya</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2310.03621v2-abstract-short" style="display: inline;"> Infrared (IR) dimension function $d_\text{IR}(位)$ characterizes the space effectively utilized by QCD quarks at Dirac scale $位$, and indirectly the space occupied by glue fields. It was proposed that its non-analytic behavior in thermal infrared phase reflects the separation of QCD system into an IR component and an independent bulk. Here we study the ``plateau modes" in IR component, whose dimens… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.03621v2-abstract-full').style.display = 'inline'; document.getElementById('2310.03621v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2310.03621v2-abstract-full" style="display: none;"> Infrared (IR) dimension function $d_\text{IR}(位)$ characterizes the space effectively utilized by QCD quarks at Dirac scale $位$, and indirectly the space occupied by glue fields. It was proposed that its non-analytic behavior in thermal infrared phase reflects the separation of QCD system into an IR component and an independent bulk. Here we study the ``plateau modes" in IR component, whose dimensional properties were puzzling. Indeeed, in the recent metal-to-critical scenario of transition to IR phase, this low-dimensional plateau connects the Anderson-like mobility edge $位_\text{IR}=0$ in Dirac spectrum with mobility edges $\pm 位_\text{A}$. For this structure to be truly Anderson-like, plateau modes have to be exponentially localized, implying that both the effective distances $L_\text{eff} \propto L^纬$ and the effective volumes $V_\text{eff} \propto L^{d_\text{IR}}$ in these modes grow slower than any positive power of IR cutoff $L$. Although $纬=0$ was confirmed in the plateau, it was found that $d_\text{IR}\approx 1$. Here we apply the recently proposed multidimension technique to the problem. We conclude that a plateau mode of pure-glue QCD at UV cutoff $a \!=\! 0.085\,$fm occupies a subvolume of IR dimension zero with probability at least 0.9999, substantiating this aspect of metal-to-critical scenario to a respective degree. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.03621v2-abstract-full').style.display = 'none'; document.getElementById('2310.03621v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 7 figures; v2: minor improvements, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 109, 014501 (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.09459">arXiv:2305.09459</a> <span> [<a href="https://arxiv.org/pdf/2305.09459">pdf</a>, <a href="https://arxiv.org/format/2305.09459">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Separation of Infrared and Bulk in Thermal QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Meng%2C+X">Xiao-Lan Meng</a>, <a href="/search/hep-lat?searchtype=author&query=Sun%2C+P">Peng Sun</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K">Keh-Fei Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+G">Gen Wang</a>, <a href="/search/hep-lat?searchtype=author&query=Yang%2C+Y">Yi-Bo Yang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.09459v4-abstract-short" style="display: inline;"> A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N$_f$=0) and ``real-world" (N$_f$=2+1 at physical quark masses) QCD. In this {\it IR phase}, elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QC… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.09459v4-abstract-full').style.display = 'inline'; document.getElementById('2305.09459v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.09459v4-abstract-full" style="display: none;"> A new thermal regime of QCD, featuring decoupled scale-invariant infrared glue, has been proposed to exist both in pure-glue (N$_f$=0) and ``real-world" (N$_f$=2+1 at physical quark masses) QCD. In this {\it IR phase}, elementary degrees of freedom flood the infrared, forming a distinct component independent from the bulk. This behavior necessitates non-analyticities in the theory. In pure-glue QCD, such non-analyticities have been shown to arise via Anderson-like mobility edges in Dirac spectra ($位_{\rm IR} \!=\! 0$, $\pm 位_\text{A} \!\neq\! 0$), as manifested in the dimension function $d_{\rm IR} (位)$. Here, we present the first evidence, based on lattice QCD calculation at $a$=0.105 fm, that this mechanism is also at work in real-world QCD, thus supporting the existence of the proposed IR regime in nature. An important aspect of our results is that, while at $T\!=\!234\,$MeV we find a dimensional jump between zero modes and lowest near-zero modes very close to unity ($d_{\rm IR} \!=\!3$ to $d_{\rm IR} \!\simeq\! 2$), similar to the IR phase of pure-glue QCD, at $T\!=\!187\,$MeV we observe a continuous $位$-dependence. This suggests that thermal states just {\it above} the chiral crossover are non-analytically (in $T$) connected to thermal state at $T\!=\!234\,$MeV, supporting the key original proposition that the transition into the IR regime occurs at a temperature strictly above the chiral crossover. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.09459v4-abstract-full').style.display = 'none'; document.getElementById('2305.09459v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, 11 figures, version accepted by JHEP</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.09806">arXiv:2212.09806</a> <span> [<a href="https://arxiv.org/pdf/2212.09806">pdf</a>, <a href="https://arxiv.org/format/2212.09806">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.3390/e25111557">10.3390/e25111557 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Topological Dimensions from Disorder and Quantum Mechanics? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Marko%C5%A1%2C+P">Peter Marko拧</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.09806v1-abstract-short" style="display: inline;"> We have recently shown that critical Anderson electron in $D=3$ dimensions effectively occupies a spatial region of infrared (IR) scaling dimension $d_\text{IR} \approx 8/3$. Here we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probability, such that points comprising a region are of similar relevance, and calculate the IR scaling… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.09806v1-abstract-full').style.display = 'inline'; document.getElementById('2212.09806v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.09806v1-abstract-full" style="display: none;"> We have recently shown that critical Anderson electron in $D=3$ dimensions effectively occupies a spatial region of infrared (IR) scaling dimension $d_\text{IR} \approx 8/3$. Here we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probability, such that points comprising a region are of similar relevance, and calculate the IR scaling dimension $d$ of each. This allows us to infer the probability density $p(d)$ for dimension $d$ to be accessed by electron. We find that $p(d)$ has a strong peak at $d$ very close to 2. In fact, our data suggests that $p(d)$ is non-zero on the interval $[d_\text{min}, d_\text{max}] \approx [4/3,8/3]$ and may develop a discrete part ($未$-function) at $d=2$ in infinite-volume limit. The latter invokes the possibility that combination of quantum mechanics and pure disorder can lead to emergence of topological dimensions. Although $d_\text{IR}$ is based on effective counting of which $p(d)$ has no a priori knowledge, $d_\text{IR} \ge d_\text{max}$ is an exact feature of the ensuing formalism. Possible connection of our results to recent findings of $d_\text{IR} \approx 2$ in Dirac near-zero modes of thermal quantum chromodynamics is emphasized. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.09806v1-abstract-full').style.display = 'none'; document.getElementById('2212.09806v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Entropy 25(11), 2023, 1557 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.13569">arXiv:2207.13569</a> <span> [<a href="https://arxiv.org/pdf/2207.13569">pdf</a>, <a href="https://arxiv.org/format/2207.13569">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physleta.2023.128735">10.1016/j.physleta.2023.128735 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Low-Dimensional Life of Critical Anderson Electron </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Marko%C5%A1%2C+P">Peter Marko拧</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.13569v3-abstract-short" style="display: inline;"> We show that critical Anderson electron in 3 dimensions is present in its spatial effective support, which was recently determined to be a region of fractal dimension $\approx \! 8/3$, with probability 1 in infinite volume. Hence, its physics is fully confined to space of this lower dimension. Stated differently, effective description of space occupied by critical Anderson electron becomes a full… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.13569v3-abstract-full').style.display = 'inline'; document.getElementById('2207.13569v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.13569v3-abstract-full" style="display: none;"> We show that critical Anderson electron in 3 dimensions is present in its spatial effective support, which was recently determined to be a region of fractal dimension $\approx \! 8/3$, with probability 1 in infinite volume. Hence, its physics is fully confined to space of this lower dimension. Stated differently, effective description of space occupied by critical Anderson electron becomes a full description in infinite volume. We then show that it is a general feature of the effective counting dimension underlying these concepts, that its subnominal value implies an exact description by effective support. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.13569v3-abstract-full').style.display = 'none'; document.getElementById('2207.13569v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages, 2 figures; v2: fixes minor glitches; v3: published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physics Letters A 467 (2023) 128735 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2205.11520">arXiv:2205.11520</a> <span> [<a href="https://arxiv.org/pdf/2205.11520">pdf</a>, <a href="https://arxiv.org/format/2205.11520">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.3390/e25030482">10.3390/e25030482 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Counting-Based Effective Dimension and Discrete Regularizations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Marko%C5%A1%2C+P">Peter Marko拧</a>, <a href="/search/hep-lat?searchtype=author&query=Mendris%2C+R">Robert Mendris</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2205.11520v2-abstract-short" style="display: inline;"> Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum, structure does not enter via geometry of fixed sets but is encoded in probability distributions on associated spaces. The question then arises whether a robust notion o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.11520v2-abstract-full').style.display = 'inline'; document.getElementById('2205.11520v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2205.11520v2-abstract-full" style="display: none;"> Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum, structure does not enter via geometry of fixed sets but is encoded in probability distributions on associated spaces. The question then arises whether a robust notion of fractal measure-based dimension exists for structures represented in this way. Starting from effective number theory, we construct all counting-based schemes to select effective supports on collections of objects with probabilities and associate the effective counting dimension (ECD) with each. We then show that ECD is scheme-independent and, thus, a well-defined measure-based dimension with meaning analogous to the Minkowski dimension of fixed sets. In physics language, ECD characterizes probabilistic descriptions arising in a theory or model via discrete ``regularization''. For example, our analysis makes recent surprising results on effective spatial dimensions in quantum chromodynamics and Anderson models well founded. We discuss how to assess the reliability of regularization removals in practice and perform such analysis in the context of 3d Anderson criticality. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2205.11520v2-abstract-full').style.display = 'none'; document.getElementById('2205.11520v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 May, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 1 figure; v2: published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Entropy 25(3), 2023, 482 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.11266">arXiv:2110.11266</a> <span> [<a href="https://arxiv.org/pdf/2110.11266">pdf</a>, <a href="https://arxiv.org/format/2110.11266">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.129.106601">10.1103/PhysRevLett.129.106601 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Super-Universality in Anderson Localization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Marko%C5%A1%2C+P">Peter Marko拧</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.11266v2-abstract-short" style="display: inline;"> We calculate the effective spatial dimension $d_\text{IR}$ of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value $d_\text{IR} \!=\! 2.665(3) \!\approx\! 8/3$. The existence of such a unique marker may help identify natural processes driven by Anderson localization, and prov… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.11266v2-abstract-full').style.display = 'inline'; document.getElementById('2110.11266v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.11266v2-abstract-full" style="display: none;"> We calculate the effective spatial dimension $d_\text{IR}$ of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value $d_\text{IR} \!=\! 2.665(3) \!\approx\! 8/3$. The existence of such a unique marker may help identify natural processes driven by Anderson localization, and provide new insight into the spatial geometry of Anderson transitions. The recently introduced $d_\text{IR}$ is a measure-based dimension of Minkowski/Hausdorff type, designed to characterize probability-induced effective subsets. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.11266v2-abstract-full').style.display = 'none'; document.getElementById('2110.11266v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 2 figures; v2: minor changes, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 129, 106601 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.04833">arXiv:2110.04833</a> <span> [<a href="https://arxiv.org/pdf/2110.04833">pdf</a>, <a href="https://arxiv.org/format/2110.04833">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2022.137370">10.1016/j.physletb.2022.137370 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Anderson Metal-to-Critical Transition in QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.04833v2-abstract-short" style="display: inline;"> A picture of thermal QCD phase change based on the analogy with metal-to-insulator transition of Anderson type was proposed in the past. In this picture, a low-$T$ thermal state is akin to a metal with deeply infrared (IR) Dirac modes abundant and extended, while a high-$T$ state is akin to an insulator with IR modes depleted and localized below a mobility edge $位_{\text A} > 0$. Here we argue tha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.04833v2-abstract-full').style.display = 'inline'; document.getElementById('2110.04833v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.04833v2-abstract-full" style="display: none;"> A picture of thermal QCD phase change based on the analogy with metal-to-insulator transition of Anderson type was proposed in the past. In this picture, a low-$T$ thermal state is akin to a metal with deeply infrared (IR) Dirac modes abundant and extended, while a high-$T$ state is akin to an insulator with IR modes depleted and localized below a mobility edge $位_{\text A} > 0$. Here we argue that, while $位_{\text A}$ exists in QCD, a high-$T$ state is not an insulator in such an analogy. Rather, it is a critical state arising due to a new singular mobility edge at $位_{\text IR}=0$. This new mobility edge appears upon the transition into the recently proposed IR phase. As a key part of such a metal-to-critical scenario, we present evidence using pure-glue QCD that deeply infrared Dirac modes in the IR phase extend to arbitrarily long distances. This is consistent with our previous suggestion that the IR phase supports scale invariance in the infrared. We discuss the role of Anderson-like aspects in this thermal regime and emphasize that the combination of gauge field topology and disorder plays a key role in shaping its IR physics. Our conclusions are conveyed by the structure of Dirac spectral non-analyticities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.04833v2-abstract-full').style.display = 'none'; document.getElementById('2110.04833v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 5 figures; v2: minor improvements, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physics Letters B 833 (2022) 137370 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.05607">arXiv:2103.05607</a> <span> [<a href="https://arxiv.org/pdf/2103.05607">pdf</a>, <a href="https://arxiv.org/format/2103.05607">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.127.052303">10.1103/PhysRevLett.127.052303 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Unusual Features of QCD Low-Energy Modes in IR Phase </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.05607v2-abstract-short" style="display: inline;"> It was recently proposed that there is a phase in thermal QCD (IR phase) at temperatures well above the chiral crossover, featuring elements of scale invariance in the infrared (IR). Here we study the effective spatial dimensions, $d_{IR}$, of Dirac low-energy modes in this phase, in the context of pure-glue QCD. Our $d_{IR}$ is based on the scaling of mode support toward thermodynamic limit, and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.05607v2-abstract-full').style.display = 'inline'; document.getElementById('2103.05607v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.05607v2-abstract-full" style="display: none;"> It was recently proposed that there is a phase in thermal QCD (IR phase) at temperatures well above the chiral crossover, featuring elements of scale invariance in the infrared (IR). Here we study the effective spatial dimensions, $d_{IR}$, of Dirac low-energy modes in this phase, in the context of pure-glue QCD. Our $d_{IR}$ is based on the scaling of mode support toward thermodynamic limit, and hence is an IR probe. Ordinary extended modes, such as those at high energy, have $d_{IR}=3$. We find $d_{IR}<3$ in the spectral range whose lower edge coincides with $位_{IR}=0$, the singularity of spectral density defining the IR phase, and the upper edge with $位_A$, the previously identified Anderson-like non-analyticity. Details near $位_{IR}$ are unexpected in that only exact zero modes are $d_{IR}=3$, while a thin spectral layer near zero is $d_{IR}=2$, followed by an extended layer of $d_{IR}=1$ modes. With only integer values appearing, $d_{IR}$ may have topological origin. We find similar structure at $位_A$, and associate its adjacent thin layer ($d_{IR} >\approx 2$) with Anderson-like criticality. Our analysis reveals the manner in which non-analyticities at $位_{IR}$ and $位_A$, originally identified in other quantities, appear in $d_{IR}(位)$. This dimension structure may be important for understanding the near-perfect fluidity of the quark-gluon medium seen in accelerator experiments. The role of $位_A$ in previously conjectured decoupling of IR component is explained. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.05607v2-abstract-full').style.display = 'none'; document.getElementById('2103.05607v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 5 figures; v2: minor changes, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 127, 052303 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1907.01606">arXiv:1907.01606</a> <span> [<a href="https://arxiv.org/pdf/1907.01606">pdf</a>, <a href="https://arxiv.org/format/1907.01606">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.3390/proceedings2019013008">10.3390/proceedings2019013008 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A Different Angle on Quantum Uncertainty (Measure Angle) </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Mendris%2C+R">Robert Mendris</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1907.01606v1-abstract-short" style="display: inline;"> The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in this manner. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1907.01606v1-abstract-full" style="display: none;"> The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in this manner. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.01606v1-abstract-full').style.display = 'none'; document.getElementById('1907.01606v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 3 figures. Talk at the 7th International Conference on New Frontiers in Physics (ICNFP2018), 4-12 July 2018, Kolymbari, Crete</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Proceedings 2019, 13, 8 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1906.08047">arXiv:1906.08047</a> <span> [<a href="https://arxiv.org/pdf/1906.08047">pdf</a>, <a href="https://arxiv.org/format/1906.08047">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.100.094507">10.1103/PhysRevD.100.094507 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Possible New Phase of Thermal QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1906.08047v2-abstract-short" style="display: inline;"> Using lattice simulations, we show that there is a phase of thermal QCD, where the spectral density $蟻(位)$ of Dirac operator changes as $1/位$ for the infrared eigenvalues $位<T$. This behavior persists over the entire low energy band we can resolve accurately, over three orders of magnitude on our largest volumes. We propose that in this "IR phase", the well-known non-interacting scale invariance a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.08047v2-abstract-full').style.display = 'inline'; document.getElementById('1906.08047v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1906.08047v2-abstract-full" style="display: none;"> Using lattice simulations, we show that there is a phase of thermal QCD, where the spectral density $蟻(位)$ of Dirac operator changes as $1/位$ for the infrared eigenvalues $位<T$. This behavior persists over the entire low energy band we can resolve accurately, over three orders of magnitude on our largest volumes. We propose that in this "IR phase", the well-known non-interacting scale invariance at very short distances (UV, $位\rightarrow \infty$, asymptotic freedom), coexists with very different interacting type of scale invariance at long distances (IR, $位<T$). Such dynamics may be responsible for the unusual fluidity properties of the medium observed at RHIC and LHC. We point out its connection to the physics of Banks-Zaks fixed point, leading to the possibility of massless glueballs in the fluid. Our results lead to the classification of thermal QCD phases in terms of IR scale invariance. The ensuing picture naturally subsumes the standard chiral crossover feature at $"\!T_c\!" \,\approx 155$ MeV. Its crucial new aspect is the existence of temperature $T_{IR}$ (200 MeV $< T_{IR} < $ 250 MeV) marking the onset of IR phase and possibly a true phase transition. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.08047v2-abstract-full').style.display = 'none'; document.getElementById('1906.08047v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, 7 figures; v2: 19 pages, 7 figures, few presentation improvements, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 100, 094507 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1809.07249">arXiv:1809.07249</a> <span> [<a href="https://arxiv.org/pdf/1809.07249">pdf</a>, <a href="https://arxiv.org/ps/1809.07249">ps</a>, <a href="https://arxiv.org/format/1809.07249">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.3390/quantum3030035">10.3390/quantum3030035 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Measure Aspect of Quantum Uncertainty, of Entanglement, and the Associated Entropies </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1809.07249v3-abstract-short" style="display: inline;"> Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes instead. The resulting $渭$-uncertainties are described by the effective number theory [1] whose central result, the existence of a minimal amount, leads to a well… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.07249v3-abstract-full').style.display = 'inline'; document.getElementById('1809.07249v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1809.07249v3-abstract-full" style="display: none;"> Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes instead. The resulting $渭$-uncertainties are described by the effective number theory [1] whose central result, the existence of a minimal amount, leads to a well-defined notion of intrinsic irremovable uncertainty. We derive $渭$-uncertainty formulas for arbitrary set of commuting operators, including the cases with continuous spectra. The associated entropy-like characteristics, the $渭$-entropies, convey how many degrees of freedom are effectively involved in a given measurement process. In order to construct quantum $渭$-entropies, we are led to quantum effective numbers designed to count independent, mutually orthogonal states effectively comprising a density matrix. This concept is basis-independent and leads to a measure-based characterization of entanglement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1809.07249v3-abstract-full').style.display = 'none'; document.getElementById('1809.07249v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 September, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages; v2: typos fixed, minor improvements; v3: 18 pages, appendices added, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Quantum Reports 3(3), 2021, 534 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1807.03995">arXiv:1807.03995</a> <span> [<a href="https://arxiv.org/pdf/1807.03995">pdf</a>, <a href="https://arxiv.org/format/1807.03995">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Disordered Systems and Neural Networks">cond-mat.dis-nn</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.3390/e22111273">10.3390/e22111273 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Effective Number Theory: Counting the Identities of a Quantum State </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Mendris%2C+R">Robert Mendris</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1807.03995v3-abstract-short" style="display: inline;"> Quantum physics frequently involves a need to count the states, subspaces, measurement outcomes, and other elements of quantum dynamics. However, with quantum mechanics assigning probabilities to such objects, it is often desirable to work with the notion of a "total" that takes into account their varied relevance. For example, such an effective count of position states available to a lattice elec… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.03995v3-abstract-full').style.display = 'inline'; document.getElementById('1807.03995v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1807.03995v3-abstract-full" style="display: none;"> Quantum physics frequently involves a need to count the states, subspaces, measurement outcomes, and other elements of quantum dynamics. However, with quantum mechanics assigning probabilities to such objects, it is often desirable to work with the notion of a "total" that takes into account their varied relevance. For example, such an effective count of position states available to a lattice electron could characterize its localization properties. Similarly, the effective total of outcomes in the measurement step of a quantum computation relates to the efficiency of the quantum algorithm. Despite a broad need for effective counting, a well-founded prescription has not been formulated. Instead, the assignments that do not respect the measure-like nature of the concept, such as versions of the participation number or exponentiated entropies, are used in some areas. Here, we develop the additive theory of effective number functions (ENFs), namely functions assigning consistent totals to collections of objects endowed with probability weights. Our analysis reveals the existence of a minimal total, realized by the unique ENF, which leads to effective counting with absolute meaning. Touching upon the nature of the measure, our results may find applications not only in quantum physics, but also in other quantitative sciences. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.03995v3-abstract-full').style.display = 'none'; document.getElementById('1807.03995v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 1 figure; v2: some restructuring and presentation improvements, 15 pages, 1 figure; v3: published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Entropy 22(11), 2020, 1273 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.04926">arXiv:1611.04926</a> <span> [<a href="https://arxiv.org/pdf/1611.04926">pdf</a>, <a href="https://arxiv.org/format/1611.04926">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.95.014509">10.1103/PhysRevD.95.014509 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Locality and Efficient Evaluation of Lattice Composite Fields: Overlap-Based Gauge Operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.04926v2-abstract-short" style="display: inline;"> We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such non-u… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.04926v2-abstract-full').style.display = 'inline'; document.getElementById('1611.04926v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.04926v2-abstract-full" style="display: none;"> We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such non-ultralocal operators, whose computational cost is volume-indepenent at fixed accuracy, and only grows logarithmically as this accuracy approaches zero. This makes computation of useful operators, such as overlap-based topological density, practical. The key notion underlying these features is that of exponential insensitivity to distant fields, made rigorous by introducing the procedure of statistical regularization. The scales associated with insensitivity property are useful characteristics of non-local continuum operators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.04926v2-abstract-full').style.display = 'none'; document.getElementById('1611.04926v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 January, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">34 pages, 10 figures; v2: published version with few remarks added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 95, 014509 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1511.09370">arXiv:1511.09370</a> <span> [<a href="https://arxiv.org/pdf/1511.09370">pdf</a>, <a href="https://arxiv.org/format/1511.09370">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Classifying the Phases of Gauge Theories by Spectral Density of Probing Chiral Quarks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1511.09370v1-abstract-short" style="display: inline;"> We describe our recent proposal that distinct phases of gauge theories with fundamental quarks translate into specific types of low-energy behavior in Dirac spectral density. The resulting scenario is built around new evidence substantiating the existence of a phase characterized by bimodal (anomalous) density, and corresponding to deconfined dynamics with broken valence chiral symmetry. We argue… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.09370v1-abstract-full').style.display = 'inline'; document.getElementById('1511.09370v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1511.09370v1-abstract-full" style="display: none;"> We describe our recent proposal that distinct phases of gauge theories with fundamental quarks translate into specific types of low-energy behavior in Dirac spectral density. The resulting scenario is built around new evidence substantiating the existence of a phase characterized by bimodal (anomalous) density, and corresponding to deconfined dynamics with broken valence chiral symmetry. We argue that such anomalous phase occurs quite generically in these theories, including in "real world" QCD above the crossover temperature, and in zero-temperature systems with many light flavors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.09370v1-abstract-full').style.display = 'none'; document.getElementById('1511.09370v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 7 figures. Proceedings of the 33rd International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japan</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1502.07732">arXiv:1502.07732</a> <span> [<a href="https://arxiv.org/pdf/1502.07732">pdf</a>, <a href="https://arxiv.org/format/1502.07732">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.92.045038">10.1103/PhysRevD.92.045038 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Phases of SU(3) Gauge Theories with Fundamental Quarks via Dirac Spectral Density </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1502.07732v2-abstract-short" style="display: inline;"> We propose that, in SU(3) gauge theories with fundamental quarks, confinement can be inferred from spectral density of the Dirac operator. This stems from the proposition that its possible behaviors are exhausted by three distinct types (Fig.1). The monotonic cases are standard and entail confinement with valence chiral symmetry breaking (A) or the lack of both (C,C'). The bimodal (anomalous) opti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.07732v2-abstract-full').style.display = 'inline'; document.getElementById('1502.07732v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1502.07732v2-abstract-full" style="display: none;"> We propose that, in SU(3) gauge theories with fundamental quarks, confinement can be inferred from spectral density of the Dirac operator. This stems from the proposition that its possible behaviors are exhausted by three distinct types (Fig.1). The monotonic cases are standard and entail confinement with valence chiral symmetry breaking (A) or the lack of both (C,C'). The bimodal (anomalous) option (B) was frequently regarded as an artifact (lattice or other) in previous studies, but we show for the first time that it persists in the continuum limit, and conclude that it informs of a non-confining phase with broken valence chiral symmetry. This generalization rests on the following. $(伪)$ We show that bimodality in $N_f$=0 theory past deconfinement temperature $T_c$ is stable with respect to removal of both infrared and ultraviolet cutoffs, indicating that anomalous phase is not an artifact. $(尾)$ We demonstrate that transition to bimodality in $N_f$=0 is simultaneous with the loss of confinement: anomalous phase occurs for $T_c < T < T_{ch}$, where $T_{ch}$ is the valence chiral restoration temperature. $(纬)$ Evidence is presented for thermal anomalous phase in $N_f$=2+1 QCD at physical quark masses, whose onset too coincides with the conventional "crossover $T_c$''. We conclude that the anomalous regime $T_c < T < T_{ch}$ is very likely a feature of nature's strong interactions. $(未)$ Our past studies of zero-temperature $N_f$=12 theories revealed that bimodality also arises via purely light-quark effects. As a result, we expect to encounter anomalous phase on generic paths to valence chiral restoration. We predict its existence also for $N_f$ massless flavors ($T=0$) in the range $N_f^c < N_f < N_f^{ch}$, where $N_f^c$ could be quite low. Conventional arguments would associate $N_f^{ch}$ with the onset of conformal window. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.07732v2-abstract-full').style.display = 'none'; document.getElementById('1502.07732v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 August, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 February, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 6 figures; v2: PRD version, few remarks/references added and minor reformulations made, 11 pages, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 92, 045038 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1412.1777">arXiv:1412.1777</a> <span> [<a href="https://arxiv.org/pdf/1412.1777">pdf</a>, <a href="https://arxiv.org/format/1412.1777">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Broken Valence Chiral Symmetry and Chiral Polarization of Dirac Spectrum in N$_f$=12 QCD at Small Quark Mass </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1412.1777v1-abstract-short" style="display: inline;"> The validity of recently proposed equivalence between valence spontaneous chiral symmetry breaking (vSChSB) and chiral polarization of low energy Dirac spectrum (ChP) in SU(3) gauge theory, is examined for the case of twelve mass-degenerate fundamental quark flavors. We find that the vSChSB-ChP correspondence holds for regularized systems studied. Moreover, our results suggest that vSChSB occurs i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.1777v1-abstract-full').style.display = 'inline'; document.getElementById('1412.1777v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1412.1777v1-abstract-full" style="display: none;"> The validity of recently proposed equivalence between valence spontaneous chiral symmetry breaking (vSChSB) and chiral polarization of low energy Dirac spectrum (ChP) in SU(3) gauge theory, is examined for the case of twelve mass-degenerate fundamental quark flavors. We find that the vSChSB-ChP correspondence holds for regularized systems studied. Moreover, our results suggest that vSChSB occurs in two qualitatively different circumstances: there is a quark mass $m_c$ such that for $m > m_c$ the mode condensing Dirac spectrum exhibits standard monotonically increasing density, while for $m_{ch} < m < m_c$ the peak around zero separates from the bulk of the spectrum, with density showing a pronounced depletion at intermediate scales. Valence chiral symmetry restoration may occur at yet smaller masses $m < m_{ch}$, but this has not yet been seen by overlap valence probe, leaving the $m_{ch}=0$ possibility open. The latter option could place massless N$_f$=12 theory outside of conformal window. Anomalous behavior of overlap Dirac spectrum for $m_{ch} < m < m_c$ is qualitatively similar to one observed previously in zero and few-flavor theories as an effect of thermal agitation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1412.1777v1-abstract-full').style.display = 'none'; document.getElementById('1412.1777v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 December, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 2 figures. Talk presented at Quark Confinement and the Hadron Spectrum XI, 8-12 September 2014, Saint-Petersburg, Russia</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1409.7094">arXiv:1409.7094</a> <span> [<a href="https://arxiv.org/pdf/1409.7094">pdf</a>, <a href="https://arxiv.org/format/1409.7094">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Deconfinement, Chiral Symmetry Breaking and Chiral Polarization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1409.7094v2-abstract-short" style="display: inline;"> We examine the feasibility of the proposition that there is a temperature range T$_c$ < T < T$_{ch}$ in N$_f$=0 QCD, where real Polyakov line (deconfined) vacuum exhibits valence spontaneous chiral symetry breaking and dynamical chiral polarization of Dirac eigenmodes. Detailed finite-volume analysis convincingly demonstrates the existence of such phase at fixed cutoff (a=0.085 fm). Moreover, it i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1409.7094v2-abstract-full').style.display = 'inline'; document.getElementById('1409.7094v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1409.7094v2-abstract-full" style="display: none;"> We examine the feasibility of the proposition that there is a temperature range T$_c$ < T < T$_{ch}$ in N$_f$=0 QCD, where real Polyakov line (deconfined) vacuum exhibits valence spontaneous chiral symetry breaking and dynamical chiral polarization of Dirac eigenmodes. Detailed finite-volume analysis convincingly demonstrates the existence of such phase at fixed cutoff (a=0.085 fm). Moreover, it is found that this behavior also takes place closer to the continuum limit (a=0.060 fm) without qualitative change in its properties. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1409.7094v2-abstract-full').style.display = 'none'; document.getElementById('1409.7094v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 November, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 September, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 6 figures; v2: Fig.3 fixed. Talk presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, Columbia University, New York, NY</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1405.2968">arXiv:1405.2968</a> <span> [<a href="https://arxiv.org/pdf/1405.2968">pdf</a>, <a href="https://arxiv.org/format/1405.2968">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2014.11.018">10.1016/j.nuclphysb.2014.11.018 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1405.2968v3-abstract-short" style="display: inline;"> It was recently conjectured that, in SU(3) gauge theories with fundamental quarks, valence spontaneous chiral symmetry breaking is equivalent to condensation of local dynamical chirality and appearance of chiral polarization scale $螞_{ch}$. Here we consider more general association involving the low-energy layer of chirally polarized modes which, in addition to its width ($螞_{ch}$), is also charac… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1405.2968v3-abstract-full').style.display = 'inline'; document.getElementById('1405.2968v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1405.2968v3-abstract-full" style="display: none;"> It was recently conjectured that, in SU(3) gauge theories with fundamental quarks, valence spontaneous chiral symmetry breaking is equivalent to condensation of local dynamical chirality and appearance of chiral polarization scale $螞_{ch}$. Here we consider more general association involving the low-energy layer of chirally polarized modes which, in addition to its width ($螞_{ch}$), is also characterized by volume density of participating modes ($惟$) and the volume density of total chirality ($惟_{ch}$). Few possible forms of the correspondence are discussed, paying particular attention to singular cases where $惟$ emerges as the most versatile characteristic. The notion of finite-volume "order parameter", capturing the nature of these connections, is proposed. We study the effects of temperature (in N$_f$=0 QCD) and light quarks (in N$_f$=12), both in the regime of possible symmetry restoration, and find agreement with these ideas. In N$_f$=0 QCD, results from several volumes indicate that, at the lattice cutoff studied, the deconfinement temperature $T_c$ is strictly smaller than the overlap-valence chiral transition temperature $T_{ch}$ in real Polyakov line vacuum. Somewhat similar intermediate phase (in quark mass) is also seen in N$_f$=12. It is suggested that deconfinement in N$_f$=0 is related to indefinite convexity of absolute X-distributions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1405.2968v3-abstract-full').style.display = 'none'; document.getElementById('1405.2968v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 February, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 May, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">45 pages, 20 figures; v2: reduced the size of submission and fixed references to appendices; v3: minor changes - published form</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl. Phys. B891, 1 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.0905">arXiv:1302.0905</a> <span> [<a href="https://arxiv.org/pdf/1302.0905">pdf</a>, <a href="https://arxiv.org/ps/1302.0905">ps</a>, <a href="https://arxiv.org/format/1302.0905">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Dynamical Local Chirality and Chiral Symmetry Breaking </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.0905v1-abstract-short" style="display: inline;"> We present some of the reasoning and results substantiating the notion that spontaneous chiral symmetry breaking (SChSB) in QCD is encoded in local chiral properties of Dirac eigenmodes. Such association is possible when viewing chirality as a dynamical effect, measured with respect to the benchmark of statistically independent left-right components. Following this rationale leads to describing lo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.0905v1-abstract-full').style.display = 'inline'; document.getElementById('1302.0905v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.0905v1-abstract-full" style="display: none;"> We present some of the reasoning and results substantiating the notion that spontaneous chiral symmetry breaking (SChSB) in QCD is encoded in local chiral properties of Dirac eigenmodes. Such association is possible when viewing chirality as a dynamical effect, measured with respect to the benchmark of statistically independent left-right components. Following this rationale leads to describing local chiral behavior by a taylor-made correlation, namely the recently introduced correlation coefficient of polarization C_A. In this language, correlated modes (C_A>0) show dynamical preference for local chirality while anti-correlated modes (C_A<0) favor anti-chirality. Our conclusion is that SChSB in QCD can be viewed as dominance of low-energy correlation (chirality) over anti-correlation (anti-chirality) of Dirac sea. The spectral range of local chirality, chiral polarization scale Lambda_ch, is a dynamically generated scale in the theory associated with SChSB. One implication of these findings is briefly discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.0905v1-abstract-full').style.display = 'none'; document.getElementById('1302.0905v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 4 figures. Talk given at "Quark Confinement and the Hadron Spectrum X", Munich, Germany, Oct. 8-12, 2012</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Proceedings of Science (Confinement X) 079 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1211.3728">arXiv:1211.3728</a> <span> [<a href="https://arxiv.org/pdf/1211.3728">pdf</a>, <a href="https://arxiv.org/ps/1211.3728">ps</a>, <a href="https://arxiv.org/format/1211.3728">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1088/1742-6596/432/1/012034">10.1088/1742-6596/432/1/012034 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Chiral polarization scale of QCD vacuum and spontaneous chiral symmetry breaking </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1211.3728v1-abstract-short" style="display: inline;"> It has recently been found that dynamics of pure glue QCD supports the low energy band of Dirac modes with local chiral properties qualitatively different from that of a bulk: while bulk modes suppress chirality relative to statistical independence between left and right, the band modes enhance it. The width of such chirally polarized zone - chiral polarization scale Lambda_ch - has been shown to… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.3728v1-abstract-full').style.display = 'inline'; document.getElementById('1211.3728v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1211.3728v1-abstract-full" style="display: none;"> It has recently been found that dynamics of pure glue QCD supports the low energy band of Dirac modes with local chiral properties qualitatively different from that of a bulk: while bulk modes suppress chirality relative to statistical independence between left and right, the band modes enhance it. The width of such chirally polarized zone - chiral polarization scale Lambda_ch - has been shown to be finite in the continuum limit at fixed physical volume. Here we present evidence that Lambda_ch remains non-zero also in the infinite volume, and is therefore a dynamical scale in the theory. Our experiments in N_f=2+1 QCD support the proposition that the same holds in the massless limit, connecting Lambda_ch to spontaneous chiral symmetry breaking. In addition, our results suggest that thermal agitation in quenched QCD destroys both chiral polarization and condensation of Dirac modes at the same temperature T_ch > T_c. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.3728v1-abstract-full').style.display = 'none'; document.getElementById('1211.3728v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 November, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 4 figures. Proceedings of "Extreme QCD" workshop, Washington, DC, Aug 21-23 2012</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1211.2601">arXiv:1211.2601</a> <span> [<a href="https://arxiv.org/pdf/1211.2601">pdf</a>, <a href="https://arxiv.org/format/1211.2601">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Chiral Polarization Scale at Finite Temperature </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1211.2601v1-abstract-short" style="display: inline;"> We study the chiral polarization properties of low-lying Dirac eigenmodes at finite temperature using the overlap operator. Results for pure gauge theory on both sides of deconfinement phase transition are presented. We find that the polarization scale decreases as we increase the temperature, but it remains non-zero as we cross in the deconfined phase and vanishes only when $T\approx 1.4 T_c$. Th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.2601v1-abstract-full').style.display = 'inline'; document.getElementById('1211.2601v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1211.2601v1-abstract-full" style="display: none;"> We study the chiral polarization properties of low-lying Dirac eigenmodes at finite temperature using the overlap operator. Results for pure gauge theory on both sides of deconfinement phase transition are presented. We find that the polarization scale decreases as we increase the temperature, but it remains non-zero as we cross in the deconfined phase and vanishes only when $T\approx 1.4 T_c$. This is caused by the presence of near-zero modes which, we find, are chirally polarized. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.2601v1-abstract-full').style.display = 'none'; document.getElementById('1211.2601v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 November, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 5 figures, Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PoS(Lattice 2012)210 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1210.7849">arXiv:1210.7849</a> <span> [<a href="https://arxiv.org/pdf/1210.7849">pdf</a>, <a href="https://arxiv.org/ps/1210.7849">ps</a>, <a href="https://arxiv.org/format/1210.7849">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2013.03.041">10.1016/j.physletb.2013.03.041 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spontaneous Chiral Symmetry Breaking as Condensation of Dynamical Chirality </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1210.7849v2-abstract-short" style="display: inline;"> The occurrence of spontaneous chiral symmetry breaking (SChSB) is equivalent to sufficient abundance of Dirac near-zeromodes. However, dynamical mechanism leading to breakdown of chiral symmetry should be naturally reflected in chiral properties of the modes. Here we offer such connection, presenting evidence that SChSB in QCD proceeds via the appearance of modes exhibiting dynamical tendency for… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1210.7849v2-abstract-full').style.display = 'inline'; document.getElementById('1210.7849v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1210.7849v2-abstract-full" style="display: none;"> The occurrence of spontaneous chiral symmetry breaking (SChSB) is equivalent to sufficient abundance of Dirac near-zeromodes. However, dynamical mechanism leading to breakdown of chiral symmetry should be naturally reflected in chiral properties of the modes. Here we offer such connection, presenting evidence that SChSB in QCD proceeds via the appearance of modes exhibiting dynamical tendency for local chiral polarization. These modes form a band of finite width Lambda_ch (chiral polarization scale) around the surface of otherwise anti--polarized Dirac sea, and condense. Lambda_ch characterizes the dynamics of the breaking phenomenon and can be converted to a quark mass scale, thus offering conceptual means to determine which quarks of nature are governed by broken chiral dynamics. It is proposed that, within the context of SU(3) gauge theories with fundamental Dirac quarks, mode condensation is equivalent to chiral polarization. This makes Lambda_ch an "order parameter" of SChSB, albeit without local dynamical field representation away from chiral limit. Several uses of these features, both at zero and finite temperature, are discussed. Our initial estimates are Lambda_ch~150 MeV (N_f=0), Lambda_ch~80 MeV (N_f=2+1, physical point), and that the strange quark is too heavy to be crucially influenced by broken chiral symmetry. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1210.7849v2-abstract-full').style.display = 'none'; document.getElementById('1210.7849v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 May, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 October, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 5 figures; v2: very minor changes, published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B722:160-166,2013 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1111.3897">arXiv:1111.3897</a> <span> [<a href="https://arxiv.org/pdf/1111.3897">pdf</a>, <a href="https://arxiv.org/format/1111.3897">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Absolute X-distribution and self-duality </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1111.3897v1-abstract-short" style="display: inline;"> Various models of QCD vacuum predict that it is dominated by excitations that are predominantly self-dual or anti-self-dual. In this work we look at the tendency for self-duality in the case of pure-glue SU(3) gauge theory using the overlap-based definition of the field-strength tensor. To gauge this property, we use the absolute X-distribution method which is designed to quantify the dynamical te… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.3897v1-abstract-full').style.display = 'inline'; document.getElementById('1111.3897v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1111.3897v1-abstract-full" style="display: none;"> Various models of QCD vacuum predict that it is dominated by excitations that are predominantly self-dual or anti-self-dual. In this work we look at the tendency for self-duality in the case of pure-glue SU(3) gauge theory using the overlap-based definition of the field-strength tensor. To gauge this property, we use the absolute X-distribution method which is designed to quantify the dynamical tendency for polarization for arbitrary random variables that can be decomposed in a pair of orthogonal subspaces. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.3897v1-abstract-full').style.display = 'none'; document.getElementById('1111.3897v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 November, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Talk presented at The XXIX International Conference on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1110.2762">arXiv:1110.2762</a> <span> [<a href="https://arxiv.org/pdf/1110.2762">pdf</a>, <a href="https://arxiv.org/ps/1110.2762">ps</a>, <a href="https://arxiv.org/format/1110.2762">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2011.11.034">10.1016/j.physletb.2011.11.034 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> How Self-Dual is QCD? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1110.2762v1-abstract-short" style="display: inline;"> Vacuum characteristics quantifying dynamical tendency toward self-duality in gauge theories could be used to judge the relevance of classical solutions or the viability of classically motivated vacuum models. Here we decompose the field strength of equilibrium gauge configurations into self-dual and anti-self-dual parts, and apply absolute X-distribution method to the resulting polarization dynami… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.2762v1-abstract-full').style.display = 'inline'; document.getElementById('1110.2762v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1110.2762v1-abstract-full" style="display: none;"> Vacuum characteristics quantifying dynamical tendency toward self-duality in gauge theories could be used to judge the relevance of classical solutions or the viability of classically motivated vacuum models. Here we decompose the field strength of equilibrium gauge configurations into self-dual and anti-self-dual parts, and apply absolute X-distribution method to the resulting polarization dynamics in order to construct such characteristics. Using lattice regularization and focusing on pure-glue SU(3) gauge theory at zero temperature, we find evidence for positive but very small dynamical tendency for self-duality of vacuum in the continuum limit. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1110.2762v1-abstract-full').style.display = 'none'; document.getElementById('1110.2762v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 October, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B706:436-441,2012 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1010.5474">arXiv:1010.5474</a> <span> [<a href="https://arxiv.org/pdf/1010.5474">pdf</a>, <a href="https://arxiv.org/ps/1010.5474">ps</a>, <a href="https://arxiv.org/format/1010.5474">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Absolute Measure of Local Chirality and the Chiral Polarization Scale of the QCD Vacuum </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">Terrence Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Streuer%2C+T">Thomas Streuer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1010.5474v1-abstract-short" style="display: inline;"> The use of the absolute measure of local chirality is championed since it has a uniform distribution for randomly reshuffled chiral components so that any deviations from uniformity in the associated "X-distribution" are directly attributable to QCD-induced dynamics. We observe a transition in the qualitative behavior of this absolute X-distribution of low-lying eigenmodes which, we propose, defin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1010.5474v1-abstract-full').style.display = 'inline'; document.getElementById('1010.5474v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1010.5474v1-abstract-full" style="display: none;"> The use of the absolute measure of local chirality is championed since it has a uniform distribution for randomly reshuffled chiral components so that any deviations from uniformity in the associated "X-distribution" are directly attributable to QCD-induced dynamics. We observe a transition in the qualitative behavior of this absolute X-distribution of low-lying eigenmodes which, we propose, defines a chiral polarization scale of the QCD vacuum. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1010.5474v1-abstract-full').style.display = 'none'; document.getElementById('1010.5474v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 October, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 8 figures, Presented at the 28th International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Sardinia, Italy, June 14-19, 2010</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/10-09 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1009.4451">arXiv:1009.4451</a> <span> [<a href="https://arxiv.org/pdf/1009.4451">pdf</a>, <a href="https://arxiv.org/ps/1009.4451">ps</a>, <a href="https://arxiv.org/format/1009.4451">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.aop.2011.04.007">10.1016/j.aop.2011.04.007 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Analysis of Space-Time Structure in QCD Vacuum II: Dynamics of Polarization and Absolute X-Distribution </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">Terrence Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Streuer%2C+T">Thomas Streuer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1009.4451v3-abstract-short" style="display: inline;"> We propose a framework for quantitative evaluation of dynamical tendency for polarization in arbitrary random variable that can be decomposed into a pair of orthogonal subspaces. The method uses measures based on comparisons of given dynamics to its counterpart with statistically independent components. The formalism of previously considered X-distributions is used to express the aforementioned co… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1009.4451v3-abstract-full').style.display = 'inline'; document.getElementById('1009.4451v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1009.4451v3-abstract-full" style="display: none;"> We propose a framework for quantitative evaluation of dynamical tendency for polarization in arbitrary random variable that can be decomposed into a pair of orthogonal subspaces. The method uses measures based on comparisons of given dynamics to its counterpart with statistically independent components. The formalism of previously considered X-distributions is used to express the aforementioned comparisons, in effect putting the former approach on solid footing. Our analysis leads to definition of a suitable correlation coefficient with clear statistical meaning. We apply the method to the dynamics induced by pure-glue lattice QCD in local left-right components of overlap Dirac eigenmodes. It is found that, in finite physical volume, there exists a non-zero physical scale in the spectrum of eigenvalues such that eigenmodes at smaller (fixed) eigenvalues exhibit convex X-distribution (positive correlation), while at larger eigenvalues the distribution is concave (negative correlation). This chiral polarization scale thus separates a regime where dynamics enhances chirality relative to statistical independence from a regime where it suppresses it, and gives an objective definition to the notion of "low" and "high" Dirac eigenmode. We propose to investigate whether the polarization scale remains non-zero in the infinite volume limit, in which case it would represent a new kind of low energy scale in QCD. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1009.4451v3-abstract-full').style.display = 'none'; document.getElementById('1009.4451v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 August, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 September, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v2: 38 pages, 12 figures, author-preferred version; v3: journal-preferred version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Annals Phys.326:1941-1971,2011 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1005.5424">arXiv:1005.5424</a> <span> [<a href="https://arxiv.org/pdf/1005.5424">pdf</a>, <a href="https://arxiv.org/ps/1005.5424">ps</a>, <a href="https://arxiv.org/format/1005.5424">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.82.114501">10.1103/PhysRevD.82.114501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Overlap Valence on 2+1 Flavor Domain Wall Fermion Configurations with Deflation and Low-mode Substitution </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Li%2C+A">A. Li</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Doi%2C+T">T. Doi</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Gong%2C+M">M. Gong</a>, <a href="/search/hep-lat?searchtype=author&query=Hasenfratz%2C+A">A. Hasenfratz</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Streuer%2C+T">T. Streuer</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1005.5424v2-abstract-short" style="display: inline;"> The overlap fermion propagator is calculated on 2+1 flavor domain wall fermion gauge configurations on 16^3 x 32, 24^3 x 64 and 32^3 x 64 lattices. With HYP smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by ~ 20 times for the 16^3 x 32 lattice and ~ 80 times for the 32^3 x 64 lattice. Through the study of hyperfine splitting, we found… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.5424v2-abstract-full').style.display = 'inline'; document.getElementById('1005.5424v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1005.5424v2-abstract-full" style="display: none;"> The overlap fermion propagator is calculated on 2+1 flavor domain wall fermion gauge configurations on 16^3 x 32, 24^3 x 64 and 32^3 x 64 lattices. With HYP smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by ~ 20 times for the 16^3 x 32 lattice and ~ 80 times for the 32^3 x 64 lattice. Through the study of hyperfine splitting, we found that the O(m^2a^2) error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. The low energy constant 螖_{mix} which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach is calculated via the scalar correlator with periodic and anti-periodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by ~ 10 to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. It is found that the many-to-all meson and baryon correlators with Z_3 grid source and low eigenmode substitution is efficient in reducing errors for the correlators of both mesons and baryons. With 64-point Z_3 grid source and low-mode substitution, it can reduce the statistical errors of the light quark (m_蟺 ~ 200 - 300 MeV) meson and nucleon correlators by a factor of ~ 3-4 as compared to the point source. The Z_3 grid source itself can reduce the errors of the charmonium correlators by a factor of ~ 3. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.5424v2-abstract-full').style.display = 'none'; document.getElementById('1005.5424v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 November, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 May, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages, 18 figures, replaced with the version to be published in PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/10-01 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D82:114501,2010 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0809.2834">arXiv:0809.2834</a> <span> [<a href="https://arxiv.org/pdf/0809.2834">pdf</a>, <a href="https://arxiv.org/ps/0809.2834">ps</a>, <a href="https://arxiv.org/format/0809.2834">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> Dominance of Sign Geometry and the Homogeneity of the Fundamental Topological Structure </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Streuer%2C+T">Thomas Streuer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0809.2834v1-abstract-short" style="display: inline;"> We propose and support the possibility that the shape of topological density 2-point function in pure-glue QCD is crucially, and possibly entirely, determined by the space-time folding (geometry) of the double-sheet sign-coherent structure of Ref.[1], while the distribution of topological density within individual sheets only determines the overall magnitude of the correlator at finite physical… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2834v1-abstract-full').style.display = 'inline'; document.getElementById('0809.2834v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0809.2834v1-abstract-full" style="display: none;"> We propose and support the possibility that the shape of topological density 2-point function in pure-glue QCD is crucially, and possibly entirely, determined by the space-time folding (geometry) of the double-sheet sign-coherent structure of Ref.[1], while the distribution of topological density within individual sheets only determines the overall magnitude of the correlator at finite physical distances. A specific manifestation of this, discussed here, is that the shape of the correlation function (encoding e.g. the masses of pseudoscalar glueballs) is reproduced upon the replacement q(x) -> sgn(q(x)), i.e. by considering the double sheet of the same space-time geometry but with constant magnitude of topological density. Combined with previous results on the fundamental topological structure, this suggests that a collective degree of freedom describing topological fluctuations of QCD vacuum can be viewed as a global space-filling homogeneous double membrane. Selected possibilities for practical uses of this are discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2834v1-abstract-full').style.display = 'none'; document.getElementById('0809.2834v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 September, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 3 figures. Presentation at Lattice 2008, Williamsburg, VA, USA</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PoS LATTICE2008:261,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0803.2744">arXiv:0803.2744</a> <span> [<a href="https://arxiv.org/pdf/0803.2744">pdf</a>, <a href="https://arxiv.org/ps/0803.2744">ps</a>, <a href="https://arxiv.org/format/0803.2744">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.78.085002">10.1103/PhysRevD.78.085002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K">Keh-Fei Liu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0803.2744v2-abstract-short" style="display: inline;"> It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge action is proportional to the trace of Ginsparg-Wilson operator D chosen to define the quark dynamics. This construction relies on the proposition that the class… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0803.2744v2-abstract-full').style.display = 'inline'; document.getElementById('0803.2744v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0803.2744v2-abstract-full" style="display: none;"> It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge action is proportional to the trace of Ginsparg-Wilson operator D chosen to define the quark dynamics. This construction relies on the proposition that the classical limit of lattice gauge operator tr D(x,x) is proportional to tr F.F(x) (up to an additive constant). Here we show this for the case of the overlap Dirac operator using both analytical and numerical methods. We carry out the same analysis also for the tensor component of D, which is similarly related to the field-strength tensor F, and obtain results identical to our previous derivation that used different approach. The corresponding proportionality constants are computed to high precision for wide range of the negative mass parameter values, and it is verified that they are the same in finite and infinite volumes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0803.2744v2-abstract-full').style.display = 'none'; document.getElementById('0803.2744v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 September, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 March, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">31 pages, 7 figures; v2: 28 pages, 5 figures, some simplification and new references, version to be published in PRD</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D78:085002,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0703010">arXiv:hep-lat/0703010</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0703010">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0703010">ps</a>, <a href="https://arxiv.org/format/hep-lat/0703010">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2007.11.010">10.1016/j.physletb.2007.11.010 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Gauge Field Strength Tensor from the Overlap Dirac Operator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">I. Horv谩th</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0703010v1-abstract-short" style="display: inline;"> We derive the classical continuum limit of the operator tr$_s 蟽_{渭谓} D^{ov}(x,x)$ with $D^{ov}$ being the overlap Dirac operator and show that it corresponds to the gauge field strength tensor $F_{渭谓}(x)$. </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0703010v1-abstract-full" style="display: none;"> We derive the classical continuum limit of the operator tr$_s 蟽_{渭谓} D^{ov}(x,x)$ with $D^{ov}$ being the overlap Dirac operator and show that it corresponds to the gauge field strength tensor $F_{渭谓}(x)$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0703010v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0703010v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 March, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/06-07 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B659:773-782,2008 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0610121">arXiv:hep-lat/0610121</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0610121">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0610121">ps</a>, <a href="https://arxiv.org/format/hep-lat/0610121">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Coherent lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0610121v1-abstract-short" style="display: inline;"> We discuss a proposal for the construction of lattice QCD with gauge action, fermionic action, theta-term, and the operators all based on the lattice Dirac operator D with exact chiral symmetry. The simplest regularization of this type uses the proposition that the classical limit of scalar gauge density associated with trace of D is (up to an additive constant) proportional to tr(FF), while the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0610121v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0610121v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0610121v1-abstract-full" style="display: none;"> We discuss a proposal for the construction of lattice QCD with gauge action, fermionic action, theta-term, and the operators all based on the lattice Dirac operator D with exact chiral symmetry. The simplest regularization of this type uses the proposition that the classical limit of scalar gauge density associated with trace of D is (up to an additive constant) proportional to tr(FF), while the corresponding operator is local. More general formulations from this class are considered with the aim of exposing interrelations between gauge and fermionic aspects of QCD which are otherwise hidden in generic formulations. Possible utility of these formulations for exploring QCD vacuum structure is emphasized. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0610121v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0610121v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 October, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages. Talk presented at Lattice 2006 (Chiral Symmetry)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PoSLAT2006:053,2006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0609034">arXiv:hep-lat/0609034</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0609034">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0609034">ps</a>, <a href="https://arxiv.org/format/hep-lat/0609034">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> On the Locality and Scaling of Overlap Fermions at Coarse Lattice Spacings </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">Terrence Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">Nilmani Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J">Jianbo Zhang</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Ying Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S">Shao-Jing Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">Frank X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K">Keh-Fei Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">Sonali Tamhankar</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0609034v1-abstract-short" style="display: inline;"> The overlap fermion offers the considerable advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly tha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0609034v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0609034v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0609034v1-abstract-full" style="display: none;"> The overlap fermion offers the considerable advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that, with appropriate choice of negative Wilson's mass, the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero in physical units in the continuum limit). In particular, our direct results contradict recent speculation that an inverse lattice spacing of 1 GeV is too low to have satisfactory localization. Furthermore, hadronic masses (available on the two coarser lattices) scale very well. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0609034v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0609034v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 September, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, 18 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/06-11 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-ph/0607110">arXiv:hep-ph/0607110</a> <span> [<a href="https://arxiv.org/pdf/hep-ph/0607110">pdf</a>, <a href="https://arxiv.org/ps/hep-ph/0607110">ps</a>, <a href="https://arxiv.org/format/hep-ph/0607110">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.76.114505">10.1103/PhysRevD.76.114505 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Scalar Mesons a0(1450) and sigma(600) from Lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">Nilmani Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">S. Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-ph/0607110v2-abstract-short" style="display: inline;"> We study the a0 and sigma mesons with the overlap fermion in the chiral regime with the pion mass as low as 182 MeV in the quenched approximation. After the eta'pi ghost states are separated, we find that the a0 mass with q\bar{q} interpolation field to be almost independent of the quark mass in the region below the strange quark mass. The chirally extrapolated results are consistent with a0(145… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-ph/0607110v2-abstract-full').style.display = 'inline'; document.getElementById('hep-ph/0607110v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-ph/0607110v2-abstract-full" style="display: none;"> We study the a0 and sigma mesons with the overlap fermion in the chiral regime with the pion mass as low as 182 MeV in the quenched approximation. After the eta'pi ghost states are separated, we find that the a0 mass with q\bar{q} interpolation field to be almost independent of the quark mass in the region below the strange quark mass. The chirally extrapolated results are consistent with a0(1450) being the u\bar{d} meson and K0*(1430) being the u\bar{s} meson with calculated masses at 1.42+_0.13 GeV and 1.41+_ 0.12 GeV respectively. We also calculate the scalar mesonium with a tetraquark interpolation field. In addition to the two pion scattering states, we find a state at around 550 MeV. Through the study of volume dependence, we confirm that this state is a one-particle state, in contrast to the two-pion scattering states. This suggests that the observed state is a tetraquark mesonium which is quite possibly the sigma(600) meson. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-ph/0607110v2-abstract-full').style.display = 'none'; document.getElementById('hep-ph/0607110v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 October, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 July, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, 9 figures, accepted for publication in Phys. Rev. D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> JLAB-THY-06-511, UK/06-06 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D76:114505,2007 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0607031">arXiv:hep-lat/0607031</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0607031">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0607031">ps</a>, <a href="https://arxiv.org/format/hep-lat/0607031">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> A Framework for Systematic Study of QCD Vacuum Structure II: Coherent Lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0607031v3-abstract-short" style="display: inline;"> We propose the formulation of lattice QCD wherein all elements of the theory (gauge action, fermionic action, theta-term, and all operators) are constructed from a single object, namely the lattice Dirac operator D with exact chiral symmetry. Several regularizations of this type are suggested via constructing scalar densities (gauge actions) that are explicit functions of D. The simplest of thes… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0607031v3-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0607031v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0607031v3-abstract-full" style="display: none;"> We propose the formulation of lattice QCD wherein all elements of the theory (gauge action, fermionic action, theta-term, and all operators) are constructed from a single object, namely the lattice Dirac operator D with exact chiral symmetry. Several regularizations of this type are suggested via constructing scalar densities (gauge actions) that are explicit functions of D. The simplest of these is based on the proposition that classical limit of density associated with Tr D is (up to an additive constant) proportional to FF, while the corresponding operator is local. The possibilities of explicit interrelations between gauge and fermionic aspects of the theory are emphasized together with the utility of such formulations for exploring the QCD vacuum structure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0607031v3-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0607031v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 March, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 July, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">23 pages; v2: 25 pages, Sect.5 fixed, Appendix added, reference added, minor improvements; v3: 26 pages, few imprecisions fixed and few minor wording changes</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0605008">arXiv:hep-lat/0605008</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0605008">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0605008">ps</a>, <a href="https://arxiv.org/format/hep-lat/0605008">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> A Framework for Systematic Study of QCD Vacuum Structure I: Kolmogorov Entropy and the Principle of Chiral Ordering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0605008v2-abstract-short" style="display: inline;"> In this series of articles we describe a systematic approach to studying QCD vacuum structure using the methods of lattice gauge theory. Our framework incorporates four major components. (i) The recently established existence of space-time order at all scales (fundamental structure) observed directly in typical configurations of regularized path-integral ensembles. (ii) The notion of scale-depen… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0605008v2-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0605008v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0605008v2-abstract-full" style="display: none;"> In this series of articles we describe a systematic approach to studying QCD vacuum structure using the methods of lattice gauge theory. Our framework incorporates four major components. (i) The recently established existence of space-time order at all scales (fundamental structure) observed directly in typical configurations of regularized path-integral ensembles. (ii) The notion of scale-dependent vacuum structure (effective structure) providing the means for representing and quantifying the influence of fluctuations at various scales on physical observables (phenomena). (iii) The unified description of gauge and fermionic aspects of the theory which facilitates a high level of space-time order in the path-integral ensembles. (iv) The strict ``Bottom-Up'' approach wherein the process of identifying the vacuum structure proceeds inductively, using the information from valid lattice QCD ensembles as the only input. In this work we first elaborate on the meaning of the notion of space-time order in a given configuration which is conceptually at the heart of the path-integral approach to vacuum structure. It is argued that the algorithmic complexity of binary strings associated with coarse-grained descriptions of the configuration provides a relevant quantitative measure. The corresponding ensemble averages define the ranking of different lattice theories at given cutoff by the degree of space-time order generated via their dynamics. We then introduce the set of local transformations of a configuration, chiral orderings, in which the transformed gauge connection represents an effective matrix phase acquired by chiral fermion when hopping over a given link. It is proposed that chiral orderings facilitate the evolution in the set of actions which increases the degree of space-time order while preserving the physical content of the theory, and should thus be used in the search for the fundamental QCD vacuum structure. The relation to renormalization group ideas is discussed, and the first step in general formulation of effective lattice QCD realizing the notion of scale-dependent vacuum structure is given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0605008v2-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0605008v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 May, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 May, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">68 pages, 1 figure; v2: minor changes in sections 2 and 8.1</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0510075">arXiv:hep-lat/0510075</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0510075">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0510075">ps</a>, <a href="https://arxiv.org/format/hep-lat/0510075">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Locality and Scaling of Quenched Overlap Fermions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">Terrence Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">Nilmani Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J">Jianbo Zhang</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Ying Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S">Shao-Jing Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F">Frank Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">Sonali Tamhankar</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0510075v1-abstract-short" style="display: inline;"> The overlap fermion offers the tremendous advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0510075v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0510075v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0510075v1-abstract-full" style="display: none;"> The overlap fermion offers the tremendous advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero in physical units in the continuum limit). In particular, our direct results contradict recent speculation that an inverse lattice spacing of $1 {\rm GeV}$ is too low to have satisfactory localization. Furthermore, hadronic masses (available on the two coarser lattices) scale very well. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0510075v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0510075v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 October, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Lattice 2005 (chiral fermions), 6 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/05-11 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> PoS LAT2005:120,2006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0510074">arXiv:hep-lat/0510074</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0510074">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0510074">ps</a>, <a href="https://arxiv.org/format/hep-lat/0510074">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.73.014516">10.1103/PhysRevD.73.014516 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Glueball Spectrum and Matrix Elements on Anisotropic Lattices </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Morningstar%2C+C">C. Morningstar</a>, <a href="/search/hep-lat?searchtype=author&query=Peardon%2C+M">M. Peardon</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">S. Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Young%2C+B+L">B. L. Young</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0510074v1-abstract-short" style="display: inline;"> The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/蠄$ radiative decays which will help identify the glueball states in experiments. Two… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0510074v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0510074v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0510074v1-abstract-full" style="display: none;"> The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/蠄$ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0510074v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0510074v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 October, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 16 figures, revtex4</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D73:014516,2006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0507027">arXiv:hep-lat/0507027</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0507027">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0507027">ps</a>, <a href="https://arxiv.org/format/hep-lat/0507027">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2006.04.055">10.1016/j.physletb.2006.04.055 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Charmonium Spectrum from Quenched QCD with Overlap Fermions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">S. Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0507027v1-abstract-short" style="display: inline;"> We present the first study of the charmonium spectrum using overlap fermions, on quenched configurations. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $尾$ = 6.3345. We demonstrate that we have discretization errors under control at about 5%. We obtain 88(4) MeV for hyperfine splitting using the $r_0$ scale, and 121(6) MeV using the ($1\bar{P}-1\bar{S}$) sca… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0507027v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0507027v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0507027v1-abstract-full" style="display: none;"> We present the first study of the charmonium spectrum using overlap fermions, on quenched configurations. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $尾$ = 6.3345. We demonstrate that we have discretization errors under control at about 5%. We obtain 88(4) MeV for hyperfine splitting using the $r_0$ scale, and 121(6) MeV using the ($1\bar{P}-1\bar{S}$) scale. This paper raises the possibility that the discrepancy between the lattice results and the experimental value for charmonium hyperfine splitting can be resolved using overlap fermions to simulate the charm quark on lattice. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0507027v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0507027v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 July, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 9 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/05-06 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B638:55-60,2006 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0507022">arXiv:hep-lat/0507022</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0507022">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0507022">ps</a>, <a href="https://arxiv.org/format/hep-lat/0507022">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.72.114509">10.1103/PhysRevD.72.114509 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Nonperturbative renormalization of composite operators with overlap fermions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">I. Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Leinweber%2C+D+B">D. B. Leinweber</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Williams%2C+A+G">A. G. Williams</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0507022v2-abstract-short" style="display: inline;"> We compute non-perturbatively the renormalization constants of composite operators on a quenched $16^3 \times 28 $ lattice with lattice spacing $a$ = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations $Z_A = Z_V$ and $ Z_S=Z_P$ and find that they agree well {(less tha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0507022v2-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0507022v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0507022v2-abstract-full" style="display: none;"> We compute non-perturbatively the renormalization constants of composite operators on a quenched $16^3 \times 28 $ lattice with lattice spacing $a$ = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations $Z_A = Z_V$ and $ Z_S=Z_P$ and find that they agree well {(less than 1%)} above $渭$ = 1.6 GeV. %even for our lattice with a coarse lattice spacing. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the $\bar{\rm MS}$ scheme. The wave-function renormalization $Z_蠄$ is determined from the vertex function of the axial current and $Z_A$ from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the $(pa)^2$ errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0507022v2-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0507022v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2005; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 July, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages, 20 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ADP-04-01/T580; UK/04-17 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D72:114509,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0507020">arXiv:hep-lat/0507020</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0507020">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0507020">ps</a>, <a href="https://arxiv.org/format/hep-lat/0507020">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.72.114513">10.1103/PhysRevD.72.114513 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice QCD at finite density via a new canonical approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Faber%2C+M">Manfried Faber</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K">Keh-Fei Liu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0507020v2-abstract-short" style="display: inline;"> We carry out a finite density calculation based on a canonical approach which is designed to address the overlap problem. Two degenerate flavor simulations are performed using Wilson gauge action and Wilson fermions on $4^4$ lattices, at temperatures close to the critical temperature $T_c\approx 170\MeV$ and large densities (5 to 20 times nuclear matter density). In this region, we find that the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0507020v2-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0507020v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0507020v2-abstract-full" style="display: none;"> We carry out a finite density calculation based on a canonical approach which is designed to address the overlap problem. Two degenerate flavor simulations are performed using Wilson gauge action and Wilson fermions on $4^4$ lattices, at temperatures close to the critical temperature $T_c\approx 170\MeV$ and large densities (5 to 20 times nuclear matter density). In this region, we find that the algorithm works well. We compare our results with those from other approaches. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0507020v2-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0507020v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 September, 2005; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 July, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 10 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> University of Kentucky preprint UK/05-07 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D72:114513,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0506018">arXiv:hep-lat/0506018</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0506018">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0506018">ps</a>, <a href="https://arxiv.org/format/hep-lat/0506018">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.72.034506">10.1103/PhysRevD.72.034506 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Reality of the Fundamental Topological Structure in the QCD Vacuum </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0506018v1-abstract-short" style="display: inline;"> Long-range order of a specific kind has recently been found directly in configurations dominating the regularized QCD path integral. In particular, a low-dimensional global structure was identified in typical space-time distributions of topological charge defined via the overlap Dirac matrix. The presence of the order has been concluded from the fact that the structure disappears after random pe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0506018v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0506018v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0506018v1-abstract-full" style="display: none;"> Long-range order of a specific kind has recently been found directly in configurations dominating the regularized QCD path integral. In particular, a low-dimensional global structure was identified in typical space-time distributions of topological charge defined via the overlap Dirac matrix. The presence of the order has been concluded from the fact that the structure disappears after random permutation of position coordinates in measured densities. Here we complete the argument for the reality of this structure (namely the conjecture that its existence is a consequence of QCD dynamics and not an artifact of the overlap-based definition of lattice topological field) by showing that the structure ceases to exist after randomizing the space-time coordinates of the underlying gauge field. This implies that the long-range order present in the overlap-based topological density is indeed a manifestation of QCD vacuum, and that the notion of the fundamental structure (structure involving relevant features at all scales) is viable. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0506018v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0506018v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 June, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev. D72 (2005) 034506 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0504005">arXiv:hep-lat/0504005</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0504005">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0504005">ps</a>, <a href="https://arxiv.org/format/hep-lat/0504005">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2005.04.076">10.1016/j.physletb.2005.04.076 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Negativity of the Overlap-Based Topological Charge Density Correlator in Pure-Glue QCD and the Non-Integrable Nature of its Contact Part </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">S. Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Thacker%2C+H+B">H. B. Thacker</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0504005v1-abstract-short" style="display: inline;"> We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge act… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0504005v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0504005v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0504005v1-abstract-full" style="display: none;"> We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge action we find that the size of the positive core is ~2a (with a being the lattice spacing) sufficiently close to the continuum limit. This result confirms that the overlap-based topological charge density is a valid local operator over realistic backgrounds contributing to the QCD path integral, and is important for the consistency of recent results indicating the existence of a low-dimensional global brane-like topological structure in the QCD vacuum. We also confirm the divergent short-distance behavior of the correlator, and the non-integrable nature of the associated contact part. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0504005v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0504005v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 April, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B617:49-59,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0501025">arXiv:hep-lat/0501025</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0501025">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0501025">ps</a>, <a href="https://arxiv.org/format/hep-lat/0501025">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physletb.2005.03.004">10.1016/j.physletb.2005.03.004 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Inherently Global Nature of Topological Charge Fluctuations in QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">S. Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Thacker%2C+H+B">H. B. Thacker</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0501025v3-abstract-short" style="display: inline;"> We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is low-dimensional and geometrically global, i.e. consisting of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0501025v3-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0501025v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0501025v3-abstract-full" style="display: none;"> We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is low-dimensional and geometrically global, i.e. consisting of connected sign-coherent regions with local dimensions 1<= d < 4, and spreading over arbitrarily large space--time distances. Here we show that the space-time structure that is responsible for the origin of topological susceptibility indeed exhibits global behavior. In particular, we show numerically that topological fluctuations are not saturated by localized concentrations of most intense topological charge density. To the contrary, the susceptibility saturates only after the space-time regions with most intense fields are included, such that geometrically global structure is already formed. We demonstrate this result both at the fundamental level (full topological density) and at low energy (effective density). The drastic mismatch between the point of fluctuation saturation (~ 50% of space-time at low energy) and that of global structure formation (<4% of space-time at low energy) indicates that the ordered space-time structure in topological charge is inherently global and that topological charge fluctuations in QCD cannot be understood in terms of individual localized pieces. Description in terms of global brane-like objects should be sought instead. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0501025v3-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0501025v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 February, 2005; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 January, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 3 figures; v2: typos corrected, minor modifications; v3: misprint in Eqs. (2,3) fixed</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Lett.B612:21-28,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0410046">arXiv:hep-lat/0410046</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0410046">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0410046">ps</a>, <a href="https://arxiv.org/format/hep-lat/0410046">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2004.12.038">10.1016/j.nuclphysb.2004.12.038 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysb.2005.03.007">10.1016/j.nuclphysb.2005.03.007 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Analysis of Space-Time Structure in QCD Vacuum I: Localization vs Global Behavior in Local Observables and Dirac Eigenmodes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0410046v4-abstract-short" style="display: inline;"> The structure of QCD vacuum can be studied from first principles using lattice-regularized theory. This line of research entered a qualitatively new phase recently, wherein the space-time structure (at least for some quantities) can be directly observed in configurations dominating the QCD path integral, i.e. without any subjective processing of typical configurations. This approach to QCD vacuu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0410046v4-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0410046v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0410046v4-abstract-full" style="display: none;"> The structure of QCD vacuum can be studied from first principles using lattice-regularized theory. This line of research entered a qualitatively new phase recently, wherein the space-time structure (at least for some quantities) can be directly observed in configurations dominating the QCD path integral, i.e. without any subjective processing of typical configurations. This approach to QCD vacuum structure does not rely on any proposed picture of QCD vacuum but rather attempts to characterize this structure in a model-independent manner, so that a coherent physical picture of the vacuum can emerge when such unbiased numerical information accumulates to a sufficient degree. An important part of this program is to develop a set of suitable quantitative characteristics describing the space-time structure in a meaningful and physically relevant manner. One of the basic pertinent issues here is whether QCD vacuum dynamics can be understood in terms of localized vacuum objects, or whether such objects behave as inherently global entities. The first direct studies of vacuum structure strongly support the latter. In this paper, we develop a formal framework which allows to answer this question in a quantitative manner. We discuss in detail how to apply this approach to Dirac eigenmodes and to basic scalar and pseudoscalar composites of gauge fields (action density and topological charge density). The approach is illustrated numerically on overlap Dirac zeromodes and near-zeromodes. This illustrative data provides direct quantitative evidence supporting our earlier arguments for the global nature of QCD Dirac eigenmodes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0410046v4-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0410046v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 February, 2005; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 October, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 5 figures; v2: reference added and typos corrected; v3: minor modifications, version to appear in Nuclear Physics B; v4: erratum: Eq. (6) fixed</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys.B710:464-484,2005; Erratum-ibid.B714:175-176,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0410002">arXiv:hep-lat/0410002</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0410002">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0410002">ps</a>, <a href="https://arxiv.org/format/hep-lat/0410002">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysbps.2004.11.377">10.1016/j.nuclphysbps.2004.11.377 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Progress on a canonical finite density algorithm </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Faber%2C+M">Manfried Faber</a>, <a href="/search/hep-lat?searchtype=author&query=Horv%C3%A1th%2C+I">Ivan Horv谩th</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K">Keh-Fei Liu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0410002v1-abstract-short" style="display: inline;"> We test the finite density algorithm in the canonical ensemble which combines the HMC update with the accept/reject step according to the ratio of the fermion number projected determinant to the unprojected one as a way of avoiding the determinant fluctuation problem. We report our preliminary results on the Polyakov loop in different baryon number sectors which exhibit deconfinement transitions… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0410002v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0410002v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0410002v1-abstract-full" style="display: none;"> We test the finite density algorithm in the canonical ensemble which combines the HMC update with the accept/reject step according to the ratio of the fermion number projected determinant to the unprojected one as a way of avoiding the determinant fluctuation problem. We report our preliminary results on the Polyakov loop in different baryon number sectors which exhibit deconfinement transitions on small lattices. The largest density we obtain around $T_c$ is an order of magnitude larger than that of nuclear matter. From the conserved vector current, we calculate the quark number and verify that the mixing of different baryon sectors is small. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0410002v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0410002v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 October, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 2 figures. Talk presented at Lattice 2004 conference. Lattice2004(non-zero)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys.Proc.Suppl.140:517-522,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0409128">arXiv:hep-lat/0409128</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0409128">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0409128">ps</a>, <a href="https://arxiv.org/format/hep-lat/0409128">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysbps.2004.11.253">10.1016/j.nuclphysbps.2004.11.253 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Charmonium Spectrum from Quenched QCD with Overlap Fermions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">S. Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0409128v1-abstract-short" style="display: inline;"> We present preliminary results using overlap fermions for the charmonium spectrum, in particular for hyperfine splitting. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $尾=6.3345$. Depending on how the scale is set, we obtain 104(5) MeV (using $1\bar{P}-1\bar{S}$) or 88(4) MeV (using $r_0$=0.5 fm) for the hyperfine splitting. </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0409128v1-abstract-full" style="display: none;"> We present preliminary results using overlap fermions for the charmonium spectrum, in particular for hyperfine splitting. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $尾=6.3345$. Depending on how the scale is set, we obtain 104(5) MeV (using $1\bar{P}-1\bar{S}$) or 88(4) MeV (using $r_0$=0.5 fm) for the hyperfine splitting. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0409128v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0409128v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 September, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">3 pages, 5 fiugres. Talk presented at Lattice 2004 (heavy)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys.Proc.Suppl.140:434-436,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0408006">arXiv:hep-lat/0408006</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0408006">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0408006">ps</a>, <a href="https://arxiv.org/format/hep-lat/0408006">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.nuclphysbps.2004.11.339">10.1016/j.nuclphysbps.2004.11.339 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Improved Measure of Local Chirality </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">Terrence Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">Andrei Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Ying Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S">Shao-Jing Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F">Frank Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">Nilmani Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Thacker%2C+H+B">Harry B. Thacker</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">Sonali Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J">Jianbo Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0408006v1-abstract-short" style="display: inline;"> It is popular to probe the structure of the QCD vacuum indirectly by studying individual fermion eigenmodes, because this provides a natural way to filter out UV fluctuations. The double-peaking in the distribution of the local chiral orientation parameter (X) has been offered as evidence, by some, in support of a particular model of the vacuum. Here we caution that the X-distribution peaking va… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0408006v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0408006v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0408006v1-abstract-full" style="display: none;"> It is popular to probe the structure of the QCD vacuum indirectly by studying individual fermion eigenmodes, because this provides a natural way to filter out UV fluctuations. The double-peaking in the distribution of the local chiral orientation parameter (X) has been offered as evidence, by some, in support of a particular model of the vacuum. Here we caution that the X-distribution peaking varies significantly with various versions of the definition of X. Furthermore, each distribution varies little from that resulting from a random reshuffling of the left-handed (and independently the right-handed) fields, which destroys any QCD-induced left-right correlation; that is, the double-peaking is mostly a phase-space effect. We propose a new universal definition of the X parameter whose distribution is uniform for randomly reshuffled fields. Any deviations from uniformity for actual data can then be directly attributable to QCD-induced dynamics. We find that the familiar double peak disappears. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0408006v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0408006v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 August, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Lattice 2004(topology), Fermilab, June 21-26, 2004; 3 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/04-19 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nucl.Phys.Proc.Suppl.140:623-625,2005 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-ph/0406196">arXiv:hep-ph/0406196</a> <span> [<a href="https://arxiv.org/pdf/hep-ph/0406196">pdf</a>, <a href="https://arxiv.org/ps/hep-ph/0406196">ps</a>, <a href="https://arxiv.org/format/hep-ph/0406196">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.70.074508">10.1103/PhysRevD.70.074508 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A study of pentaquarks on the lattice with overlap fermions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">N. Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">F. X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Alexandru%2C+A">A. Alexandru</a>, <a href="/search/hep-lat?searchtype=author&query=Bennhold%2C+C">C. Bennhold</a>, <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Y. Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S+J">S. J. Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">T. Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">I. Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K+F">K. F. Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">S. Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J+B">J. B. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-ph/0406196v3-abstract-short" style="display: inline;"> We present a quenched lattice QCD calculation of spin-1/2 five-quark states with $uudd\bar{s}$ quark content for both positive and negative parities. We do not observe any bound pentaquark state in these channels for either I = 0 or I =1. The states we found are consistent with KN scattering states which are checked to exhibit the expected volume dependence of the spectral weight. The results ar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-ph/0406196v3-abstract-full').style.display = 'inline'; document.getElementById('hep-ph/0406196v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-ph/0406196v3-abstract-full" style="display: none;"> We present a quenched lattice QCD calculation of spin-1/2 five-quark states with $uudd\bar{s}$ quark content for both positive and negative parities. We do not observe any bound pentaquark state in these channels for either I = 0 or I =1. The states we found are consistent with KN scattering states which are checked to exhibit the expected volume dependence of the spectral weight. The results are based on overlap-fermion propagators on two lattices, 12^3 x 28 and 16^3 x 28, with the same lattice spacing of 0.2 fm, and pion mass as low as ~ 180 MeV. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-ph/0406196v3-abstract-full').style.display = 'none'; document.getElementById('hep-ph/0406196v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 September, 2004; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 June, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">accepted for publication in Phys. Rev. D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/04-13 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.D70:074508,2004 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/hep-lat/0405001">arXiv:hep-lat/0405001</a> <span> [<a href="https://arxiv.org/pdf/hep-lat/0405001">pdf</a>, <a href="https://arxiv.org/ps/hep-lat/0405001">ps</a>, <a href="https://arxiv.org/format/hep-lat/0405001">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> The Sequential Empirical Bayes Method: An Adaptive Constrained-Curve Fitting Algorithm for Lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Chen%2C+Y">Ying Chen</a>, <a href="/search/hep-lat?searchtype=author&query=Dong%2C+S">Shao-Jing Dong</a>, <a href="/search/hep-lat?searchtype=author&query=Draper%2C+T">Terrence Draper</a>, <a href="/search/hep-lat?searchtype=author&query=Horvath%2C+I">Ivan Horvath</a>, <a href="/search/hep-lat?searchtype=author&query=Liu%2C+K">Keh-Fei Liu</a>, <a href="/search/hep-lat?searchtype=author&query=Mathur%2C+N">Nilmani Mathur</a>, <a href="/search/hep-lat?searchtype=author&query=Tamhankar%2C+S">Sonali Tamhankar</a>, <a href="/search/hep-lat?searchtype=author&query=Srinivasan%2C+C">Cidambi Srinivasan</a>, <a href="/search/hep-lat?searchtype=author&query=Lee%2C+F+X">Frank X. Lee</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+J">Jianbo Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="hep-lat/0405001v1-abstract-short" style="display: inline;"> We introduce the ``Sequential Empirical Bayes Method'', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-$蠂^2$ fits on separate data. This better stabilizes fits to lattice QCD overlap-fermion data at very low quark mass where {\it a priori} values are not otherwise known. Lessons learned (including caveats limiting the sco… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0405001v1-abstract-full').style.display = 'inline'; document.getElementById('hep-lat/0405001v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="hep-lat/0405001v1-abstract-full" style="display: none;"> We introduce the ``Sequential Empirical Bayes Method'', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-$蠂^2$ fits on separate data. This better stabilizes fits to lattice QCD overlap-fermion data at very low quark mass where {\it a priori} values are not otherwise known. Lessons learned (including caveats limiting the scope of the method) from studying artificial data are presented. As an illustration, from local-local two-point correlation functions, we obtain masses and spectral weights for ground and first-excited states of the pion, give preliminary fits for the $a_0$ where ghost states (a quenched artifact) must be dealt with, and elaborate on the details of fits of the Roper resonance and $S_{11}(N^{1/2-})$ previously presented elsewhere. The data are from overlap fermions on a quenched $16^3\times 28$ lattice with spatial size $La=3.2 {\rm fm}$ and pion mass as low as $\sim 180 {\rm MeV}$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('hep-lat/0405001v1-abstract-full').style.display = 'none'; document.getElementById('hep-lat/0405001v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 May, 2004; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2004. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">37 pages, 16 figures, uses apsrev.bst</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UK/04-10 </p> </li> </ol> <nav class="pagination is-small is-centered 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